The present invention relates to a diaphragm type ultrasonic transducer, ultrasonic probe, and ultrasonic imaging device.
Mainstream transducers transmitting and receiving ultra sound transmit and receive ultra sound, using piezoelectric effect and inverse piezoelectric effect of a ceramic piezoelectric element represented by PZT (lead zirconate titanate). This type of piezoelectric ceramic ultrasonic transducer currently still constitutes the majority of ultrasonic transducers in practical use. However, to take the place of this type, research and development of diaphragm type fine ultrasonic transducers having a structure in micrometer order by a semiconductor micro processing technology has been carried out since the 1990's (refer to Non-patent Document 1).
In a typical structure of such a transducer (an ultrasonic transducer 100p) is, as shown in a cross-sectional schematic view in
Hereinafter, for brevity of description, the direction where the ultrasonic transducer 100p receives ultra sound (downward direction in
As shown in
In order to form ultrasonic beams, a number of the above described transducers are disposed and arrayed, as shown in
Further, Patent Document 2 discloses a capacitive ultrasonic transducer reinforced by a stiffing layer at the central portion of a film.
Still further, Patent Document 3 discloses an acoustic transducer with a structure, arranged above a cavity, having an insulating layer part and a top electrode which are disposed within the thickness dimension of a film.
Non-patent Document 1: “A surface micromachined electrostatic ultrasonic air transducer”, Proceedings of 1994 IEEE Ultrasonics Symposium, pp. 1241-1244
Patent document 1: the specification of U.S. Pat. No. 5,870,351
Patent document 2: the specification of U.S. Pat. No. 6,426,582
Patent document 3: the specification of U.S. Pat. No. 6,271,620
However, in the technology disclosed in Patent Document 1, as shown in
Further, regarding transducer arrays, in general, the upper limits of the sizes of respective ultrasonic transducers are defined by the disposition pitch for which diffraction of ultra sound and the like is taken into account, and the lower limits of the sizes are defined from a point of view of securing radiation impedance which achieves a required radiation efficiency. Therefore, the sizes of these ultrasonic transducers are selected usually from a narrow range in designing.
Still further, since a semiconductor manufacturing technology is used for the above described conventional electrostatic transducer (described in Non-patent Document 1), masks corresponding to the planar shapes of diaphragms are used in a manufacturing process. There is a method of changing the frequency spectrum of a diaphragm, which changes the size (planar shape) of the diaphragm. However, it is necessary to design and manufacture a new mask for this method, which requires time and cost, causing a problem of decreasing the manufacturing efficiency.
Yet further, another method of changing the frequency spectrum of a diaphragm changes the thickness of the diaphragm. However, as described above, as the size of a diaphragm is limited in a narrow range, the thickness of the diaphragm which achieves a desired center frequency is substantially uniquely determined. Then, the size and thickness of the diaphragm define the sensitivity and fractional bandwidth of this ultrasonic transducer. Consequently, there has been a problem that a desired frequency spectrum, namely, a combination of a center frequency and a fractional band width cannot be realized.
Further, for the above described conventional capacitive ultrasonic transducer (refer to Patent Document 2), a diaphragm is reinforced by a stiffing layer. However, even obtaining a desired center frequency by arranging a stiffing layer, there has been a problem that the fractional bandwidth is automatically defined and a desired frequency spectrum cannot be achieved.
Still further, for the above described conventional acoustic transducer (described in Patent Document 3), a top electrode is arranged inside a diaphragm. Consequently, although the sensitivity may be improved, there has been a problem that means for obtaining a desired frequency spectrum is not provided, either.
Addressing problems, as described above, an object of the present invention is to provide an ultrasonic transducer, ultrasonic probe, and ultrasonic imaging device having a simple structure and being capable of improving the performance of transmission and reception of ultra sound.
An ultrasonic transducer in accordance with the invention includes a substrate having a first electrode inside thereof or on a surface thereof and a diaphragm having a second electrode therein or on a surface thereof, the substrate and diaphragm being disposed with a cavity therebetween.
The ultrasonic transducer is provided with at least one beam on a surface or inside of the diaphragm or the second electrode.
Other means will be described in embodiments described later.
According to the present invention, an ultrasonic transducer, ultrasonic probe, and ultrasonic imaging device are provided which have a simple structure and are capable of improving the performance of transmission and reception of ultra sound are provided.
Now, embodiments in accordance with the present invention will be described in details, referring to
Hereinafter, “a converter between electricity and ultra sound” will be referred to as “an ultrasonic transducer”, “a group of plural ultrasonic transducers in an array” as “a transducer array”, and “a member that has plural transducer arrays and transmits and receives ultra sounds to and from a specimen” as “an ultrasonic probe”. Further, “an ultrasonic imaging device” will represent “an imaging device by the use of ultra sound provided with an ultrasonic probe, image former (means for forming an image from a signal obtained by an ultrasonic probe), display (means for displaying an image), controller, and the like”.
Based on control by a transmission/reception sequence controller 201 programmed in advance, a transmission delay and weight selector 203 selects the values of a transmission delay time and a weight function for each channel to be supplied to a transmission beam-former 204. According to these values, the transmission beam-former 204 supplies an electro-acoustic conversion element 101 with transmission pulses through plural switches 205 for switching transmission/reception waves. Herein, an electro-acoustic conversion element 101 is also applied with a bias voltage by a bias voltage controller 202. As a result, the electro-acoustic conversion element 101 transmits ultra sound to a specimen, not shown here.
Then, the ultra sounds having been reflected by scatterers in the specimen and thereby reflected are partially received back by the electro-acoustic conversion element 101. A transmission/reception sequence controller 201 then controls a reception beam-former 206 after a predetermined time has elapsed from the timing of transmission so as to start a reception mode. The predetermined time described above, in a case of obtaining an image from a depth of a specimen deeper than 1 mm for example, is the turn around time for a sound to return a distance of 1 mm. The mode does not change to the reception mode immediately after transmission because the amplitude of the reception voltage is extremely smaller than the amplitude of the transmission voltage, being one hundredth to one thousandth. The reception beam-former 206 continuously controls the delay time and a weight function, corresponding to the arrival time of each reflected ultra sound, which is so-called a dynamic focus. Data after dynamic focus is converted into an image signal by image forming means including, for example, a filter 207, envelope detector 208, and scan converter 209, and then displayed on a display 210 as an ultrasonic tomographic image.
One of the basic characteristics which are significant in putting ultrasonic transducers in various practical uses is frequency spectrum represented by a center frequency and a fractional bandwidth. A center frequency fc is a frequency with the highest electromechanical conversion efficiency (sensitivity). A fractional bandwidth fh is, for example in a case of 3 dB width, defined as a difference between two frequencies divided by the center frequency, wherein the sensitivity at these two frequencies is 3 dB lower than the sensitivity at the center frequency. If the fractional bandwidth is wider, a single ultrasonic transducer can be used for more various frequency bands, or ultrasonic pulses with a shorter time width can be formed, which achieves advantageous characteristics, such as obtaining a high distance resolution in a case of imaging by the use of ultrasonic beams. The center frequency fc of a diaphragm type ultrasonic transducer is substantially equal to the value of resonance frequency of the diaphragm, and is accordingly represented by following Expression (1), while the fractional bandwidth fh is represented by Expression (2), wherein the stiffness and the mass of the diaphragm are represented respectively by D and m.
The stiffness and mass of an oscillation diaphragm are determined by the shape and dimensions of the oscillation diaphragm and the thickness thereof in a case of a solid material. Accordingly, in principle, by defining a proper shape and thickness of an oscillation diaphragm, a desired frequency spectrum can be obtained. However, only the two-degree-of-freedom of D and m for designing is not enough to optimize the three parameters of the center frequency, maximum value of sensitivity and fractional bandwidth.
An ultrasonic probe for an ultrasonic imaging device for photographing common two-dimensional tomographic images performs fixed focusing by an acoustic lens in the direction (short axis direction) perpendicular to the tomographic plane, and performs electronic focusing of an ultrasonic beam at a desired position on the tomographic plane, having arrayed oscillators arranged in the direction (long axis direction) along the tomographic plane. In order to form excellent ultrasonic beams, ultrasonic transducers are arrayed ideally with a width of approximately a half of the wavelength at the center frequency of beams. For example, with a center frequency of 5 MHz, ultrasonic transducers are arrayed with a width of approximately 0.15 mm. In the short axis direction, the wider the width of an ultrasonic transducer is, the narrower the beam width at the focus is, achieving a tomographic image with a higher space resolution. However, if the focus region of the fixed focus on the short axis is too narrow, it is difficult to control the focus region by electronic focusing on the long axis. Further, also in viewpoint of usability in operation by pressing the ultrasonic probe on an affected area, such as a gap between costae of a patient, the width along the short axis is preferably 7 to 8 mm.
That is, since the size of an electric element is approximately 7 to 8 mm×0.15 mm, in a case where the diameter of a diaphragm is approximately 50 μm for example, 450 (150×3=450) diaphragms are used in a state of being disposed in a single electric element. By changing the shape and material of each of the several hundred diaphragms, the fractional bandwidth of the entire single electric element can be designed more freely. There is a degree of freedom for the shape and material in principle. However, in a practical semiconductor process, a layer structure is formed on a substrate, layer by layer, it is not realistic to change the material for each transducer adjacent to one another, and it is also difficult to change the thickness of diaphragms. As a result, designing a desired fractional bandwidth by changing the diameters of diaphragms is the most practical method.
In the specification of U.S. Pat. No. 5,870,351 (Patent Document 1), an example, as shown in
From
The integrated values of the amplitudes of the reflected waves are represented by the vertical axis, and the distances between adjacent diaphragms are represented by the horizontal axis, in the graph in
In the ultrasonic transducer region as one element configured by electrically connecting diaphragm type plural ultrasonic transducers, if there is a region in which diaphragms are not formed, the pulse response is deteriorated also in the process described below.
As shown
With an ultrasonic imaging device, in a case, for example, of observing the inner structure of a blood vessel, in order to observe sites of which reflectance intensities differ from each other by 40 dB to 60 dB, such as the tissue site of the blood vessel and the lumen of the blood vessel, an image of the structure is created by compressing the brightness and with a wide dynamic range. Therefore, even if the echo of B and B′ are imperceptible, when echo of delayed B and B′ accompanies the reflectance signal A from the tissue site of the blood vessel, the echo is observed as an image inside the blood vessel, which does not allow distinction between a plaque in the blood vessel and a false image of B or the like. Judging from the dynamic range of an image by a common ultrasonic imaging device, the amplitude of a reflectance signal B is necessary to be reduced to one thousandth, namely approximately −60 dB, compared with the amplitude of a reflectance signal A. As described above, by shortening the gap between diaphragms approximately to one eightieth of a wave length, the transmission efficiency of a sound through the gap drops and effect by a reverberant sound, such as B, does not become a problem. By making the amplitude of an ultra sound entering a wafer along the path “a” small enough, the reverberant sound of B becomes small even if the reflectance ratio of the multiple reflections along the path b cannot be made small enough. As a result, it is possible to increase the degree of freedom in selection of the thicknesses and material of the adhesive to be applied to a wafer and a backside material having significant effects on the reflectance ratio of the multiple reflections along the path b, thereby improving the degree of freedom of manufacturing process.
In the present embodiment, the shapes and structures of diaphragms are adopted which are suitable for making the resonance frequencies differ from each other to widen the fractional bandwidth, while minimizing the areas of gaps between diaphragms.
Each diaphragm type ultrasonic transducer is, as shown in
Hereinafter, both or either the inner diaphragm layer 5a or the outer diaphragm layer 5b may be described merely as “diaphragm”. Further, symbols of other elements may be omitted.
As shown in
Herein, the beams 7 have a structure having a smaller width compared with the length and a shape covering only a part of the diaphragm. The beams 7 effect the resonance frequency of the diaphragm type entire ultrasonic transducer, by having the hardness conditions described below. That is, the hardness of the beams 7 is made great enough compared with the hardness of the material of the diaphragm portion forming the upper wall of the cavity 4, or the thickness of the beams 7 is made great enough compared with the thickness of the diaphragm portion. Thus, the resonance frequency of the diaphragm type entire ultrasonic transducer can be controlled by the shape and material of the beam 7. For example, with beams 7 in a simple rectangular solid shape of a width W, length 1 and thickness t, the resonance frequency fb in the thickness direction is represented by the following Expression (3). Herein, E denotes Young's Module, I denotes the cross-sectional moment, and m denotes the mass.
A beam 7 with a cross-section in a rectangle shape has a cross-sectional moment I of Wt3/3, and accordingly Equation (3) is equivalent to Equation (4). As Equation (4) is a proportional expression, coefficients are omitted.
Accordingly, if the materials of beams 7 are the same and the thickness t and length 1 are constant, the resonance frequency fb is proportional to the square root of the width W.
If the beams 7 are in a rectangular solid shape with a width of W at the marginal portion, and are in a homothetic shape of the diaphragm, as shown in
If the resonance frequency of a diaphragm can be controlled by the width W of beams 7 in such a manner, then, by packing ultrasonic transducers having diaphragms with a constant diameter and beams 7 with different widths W provided on the front surfaces or back surfaces of the respective diaphragms, as shown in
An example including materials and dimensions configuring the diaphragm type ultrasonic transducer, shown in
However, these materials and dimensions are only an example, and materials and dimensions may not be as described above. For example, assuming that the beams 7 are made of silicon nitride, the diameter of the diaphragm is 60 μm, the thickness of the film is 2 μm, and the thickness of the beams 7 is 4 μm, then, the center frequency is 7.8 MHz and −6 dB fractional bandwidth is 120% (−6 dB fractional band is 3 to 12.5 MHz) with W1 of 0.5 μm, the center frequency is 10 MHz and −6 dB fractional bandwidth is 100% (−6 dB fractional band is 5 to 15 MHz) with W2 of 4 μm, and the center frequency is 11.5 MHz and −6 dB fractional bandwidth is 96% (−6 dB fractional band is 6 to 17 MHz) with W3 of 20 μm. By optimizing the number of ultrasonic transducers having the beam width of W1, W2 and W3 (When the numbers of ultrasonic transducers having the beam width of W1 and W3 are greater than the number of ultrasonic transducers having the beam width of W2, a flatter frequency spectrum can be obtained.), −6 dB band becomes 3 to 17 MHz, that is, −6 dB fractional bandwidth becomes 140%. Compared with a known diaphragm structure with which −6 dB fractional bandwidth is approximately 100 to 120%, −6 dB fractional bandwidth is improved by 40 to 20 points.
In the example shown in
Next, a method of utilizing the wide band characteristics of an ultrasonic probe in accordance with the invention will be described.
Conventionally, as there has not been an ultrasonic probe that covers such a wide range of frequencies approximately from 2 MHz to 15 MHz, probes have been used for each of which a predetermined center frequency is set, optimizing each probe for a corresponding object site. Accordingly, a constant width among elements has been applicable, and arrays of elements of a fixed element width, such as to be a half to 75% of a wavelength, have been adopted. However, according to the invention, as shown in
Herein, in order to operate a single probe with greatly different center frequencies by switching the drive frequency depending on the depth of the object site from the body surface, the element width is necessary to be switchable. Switching of the element width is determined when an object site is selected. In a case, the element width is constant in a single imaging plane. In another case, the object site is relatively large and the element width is necessary to be changed even in a single screen depending on the place to set the object site. In still another case, the object site is extending from a vicinity of the body surface to a deep portion and the element width is necessary to be switched accompanying the movement of the focus position while receiving ultra sound. For example, a case of switching the element width while receiving ultra sound will be described, referring to a device diagram. An ultrasonic pulse in a wide band is applied from a transmission beam-former 204 in
In the transmission beam-former 204, improving signal/noise ratio by widely transmitting ultrasonic pulses is more important than increasing the space resolution by narrowing the beam. Therefore, the number of sub-elements per channel is set small, and the total aperture is set narrow. Since ultra sounds scattered in a specimen return in order of nearness to the surface of the specimen, ultra sounds return in ascending order of the propagation distance in the specimen. In a conventional technology, ultra sounds returning from the specimen are received by reception beam-former 206 through the switch 205; the delay time and weight coefficient are adjusted between channels; and a tomographic image is displayed through an envelope detector and a scan converter. On the other hand, in the invention, in a sub-element cross point switch 17 between the sub-elements 16 and the switch 205, when ultra sounds from near-surface portions are received, sub-elements are bundled in the quantity corresponding to the upper end of the band having transmitted the ultra sounds, and when ultra sounds from deeper portions are received, sub-elements are bundled in the quantity corresponding to the lower end of the band having transmitted the ultra sounds. The time is continuous from when ultra sounds are received from the near-surface portions until when ultra sounds are received from deeper portions, and accordingly, switching of the quantity of sub-elements is necessary to be carried out continuously in terms of time.
In the example in
When an operator of the ultrasonic transducer selects or inputs an object site, the range of the depth of imaging is usually determined, and the degree of attenuation of propagation medium can be estimated. Accordingly, various conditions, such as an optimum frequency, are determined. In a case, for example, of observing a relatively large body organ, such as liver or heart, the object site often extends from a near portion to a far portion even if the object site is determined. Therefore, in some cases, plural modes are applied even for a single object site, and the modes are automatically switched depending on the depth generated by a reflected echo. Sub-elements are configured by a group of diaphragm type ultrasonic transducers of which top electrodes are permanently connected by conductors. When a sub-element configures one element for beam forming, the sub-element serves as a unit of ultrasonic transducer bundled by a switchable switch. In
For example, when a diameter of diaphragms which configure a single diaphragm type ultra sound transducer is 50 μm, although it is of course impossible to adjust the element width to a range narrower than the width of one diaphragm, an element width of 0.55 mm being 75% of a wavelength at 2 MHz can be achieved by 11 rows of diaphragms with a diameter of 50 μm, and the element width of 55 μm being 75% of a wavelength at 20 MHz can be achieved by one row of diaphragms with a diameter of 50 μm, which achieves an optimal element pitch for each mode in the range from 2 MHz to 20 MHz. That is, in this case, when driving an ultrasonic probe at 2 MHz, an element width of 0.55 mm can be attained by simultaneously driving eleven bundled adjacent sub-elements as one element, and when driving an ultrasonic probe at 20 MHz, an element width of 55 μm can be attained by driving individual sub-elements independently.
This sub-element cross point switch can be mounted in the ultrasonic imaging device. However, as shown in
Now, an example of a diaphragm type transducer array using diaphragms in a shape other than a hexagonal shape will be described. Covering a transmission and reception surface of an ultrasonic probe with diaphragms with different resonance frequencies while minimizing the area of gaps between the diaphragms can be achieved also by using rectangular diaphragms. In this case, if the ratio between the longer sides and the shorter sides of the rectangular is nearly 1:1, a connected oscillation between modes corresponding to the respective sides makes the resonance mode complicated, and even though a wide band appears, the phase is not constant when the frequency spectrum is viewed in terms of both in the amplitude and the phase, resulting in different delays of respective frequency components and deterioration of the pulse spectrum along the time axis. However, by making a great difference between the length of the short sides and the length of the long sides (fore example, 1:8 or greater), diaphragms in a rectangular shape oscillates with deformation along the short sides, and accordingly, the resonance frequency is defined almost by the length of the shorter sides.
a) is a schematic plan view showing an example of an ultrasonic probe using diaphragm type ultrasonic transducers having a rectangular diaphragm.
Further, each ultrasonic transducer provided with a rectangular diaphragm has a resonance frequency defined by the length of shorter sides of the diaphragm. A single ultrasonic transducer can be obtained in which plural diaphragms, which are disposed without a gap therebetween and have different center frequencies, are simultaneously driven electrically, by selecting a combination of the lengths of the shorter sides of diaphragms such as to divide the shorter side of the electrically connected single element 14 into plural parts. For example, if W0 is 500 μm and the thickness of a film of silicon nitride is 3 μm, then, the center frequency is 7.8 MHz and the −6 dB fractional bandwidth is 120% (−6 dB fractional band is 3 to 12.5 MHz) for W1 of 60 μm, the center frequency is 10 MHz and the −6 dB fractional bandwidth is 100% (−6 dB fractional band is 5 to 15 MHz) for W2 of 50 μm, and the center frequency is 11.5 MHz and the −6 dB fractional bandwidth is 100% (−6 dB fractional band is 6 to 17 MHz) for W3 of 40 μm. By optimizing the numbers of ultrasonic transducers having the respective lengths of the shorter sides of W1, W2 and W3 (Flatter frequency spectrum is obtained with the numbers of W1 and W3 greater than the number of W2.), −6 dB band becomes 1 to 15 MHz, that is, −6 dB fractional bandwidth becomes 140%. Since −6 dB fractional bandwidth of a conventional known diaphragm structure is approximately 100 to 120%, −6 dB fractional bandwidth is improved by 20 to 40 points.
b) is a schematic plan view showing another example of an ultrasonic probe using a diaphragm type transducer array, the diaphragms being rectangular. In this ultra sound probe, plural diaphragms each of which is an element configuring the respective ultrasonic transducer are disposed in such a manner that the longer sides of them are in the same direction as the shorter sides of an electrically single element 14, in other words, in the same direction as the array direction of the transducer array. Below each diaphragm, a top electrode substantially in the same shape as the diaphragm and a cavity are provided, and a common bottom electrode arranged below the cavity and the top electrode configure a capacitor. Also by such disposition of diaphragms, it is possible to form the surface of an ultrasonic probe with plural diaphragms having different center frequencies without gaps therebetween. In disposing these diaphragms with different center frequencies, it is preferable to dispose the diaphragms with regularity as little as possible in order not to create unnecessary grating beams. Also in
Also in the present embodiment, as shown in
In the example, shown in
Also in the case of the ultrasonic transducer 100q shown in
In the above described embodiments, description has been made taking an example of one dimensional array for photographing a two dimensional tomographic image. However, also in the case of a two dimensional array or 1.5 dimensional array, plural diaphragms configure one electric element though the number of diaphragms configuring one element decreases. Therefore, it is possible to achieve a transducer array for which electric elements are disposed, wherein each of the electric elements is configured with plural diaphragms having minimized gaps therebetween and different center frequencies. This is a feature of the invention. An 1.5 dimensional array has a structure for which an array is arranged also along the direction (long axis) for scanning the position or direction of an ultrasonic beam, in other words, along the direction (short axis) perpendicular to the imaging plane, and thereby focusing along the short axis can be made variable.
Now, a third embodiment in accordance with the invention will be described, referring to
Hereinafter, for brevity of description, the same as in the case of
As shown in
The diaphragm 5 has a cavity 4 therein, and the portion covering the top of the cavity 4 forms an oscillating part 5c for generating ultra sound by oscillation. The diaphragm 5 includes the cavity 4 making the distance between the oscillating part 5c of the diaphragm 5 and the electrode 2 on the substrate 1 side, and provided with an inner diaphragm layer 5b which causes insulation so that the electrode 2 on the substrate 1 side and an electrode 3 (described later) on the diaphragm 5 side are not electrically conducted with each other even when the oscillating part 5c is deformed excessively, an outer diaphragm 5b formed such as to cover the top surface of the inner diaphragm 5a, and the electrode 3 disposed on the diaphragm 5 side and formed of the same material as the electrode 2 and in a thin film shape between the inner diaphragm layer 5a and the outer diaphragm layer 5b.
The materials of diaphragms 5 and beams 7 are those described in U.S. Pat. No. 6,359,367, for example. Examples are silicon, sapphire, any sort of glass material, polymers (such as polyimide), polysilicon, silicon nitride, silicon oxynitride, thin film metals (such as aluminum alloys, copper alloys and tungsten), spin-on-glasses (SOGs), implantable or diffused dopants and grown films such as silicon oxides and silicon nitrides.
In a steady state, the distance between the oscillating part 5c of the diaphragm 5 and the substrate 1, that is the thickness of the cavity 4 (dimension in z direction) is maintained mainly by the stiffness in the upper and lower direction (z direction) of both or either the inner diaphragm layer 5a or the outer diaphragm layer 5b. Further, this stiffness is reinforced in a predetermined direction by the beams 7.
That is, a significant feature of an ultrasonic transducer 100 in the present embodiment is that beams 7 are arranged on a diaphragm 5, and the stiffness of the diaphragm 5 is adjusted. For the transducer 100, a desired combination of a resonance frequency fb and a fractional bandwidth fh can be achieved by appropriately setting the combination of the thickness (the length along z direction) of the diaphragm 5 and the thickness (the length in z direction) of the beams 7.
In order to change the planar shape (dimensions in x direction and y direction) of the diaphragm 5 and beams 7, different masks (not shown) are required in the manufacturing process. However, these thicknesses (dimension in z direction) can be changed by just changing the control of the manufacturing process, such as adjusting the time for depositing a material of the diaphragm to a desired thickness, which brings an advantage of manufacturing by the same manufacturing equipment.
When briefly described as an electric element, this ultrasonic transducer 100 acts as a variable capacity capacitor having an electrode 2 on the substrate 1 side and an electrode 3 on the diaphragm 5 side, the both electrodes serving as polar plates, with the cavity 4 disposed therebetween and functioning as a dielectric. Specifically, when a force is applied to the diaphragm 5, the diaphragm is displaced and thereby the distance between the electrode 2 and electrode 3 changes, thus the capacitance of the capacitor changes. When a difference in potential is applied to the electrode 2 and electrode 3, respective opposite charges are accumulated in them to cause forces acting on each other, and thus the diaphragm 5 is displaced. That is, the ultrasonic transducer 100 is an electro-acoustic conversion element that converts a high frequency electric signal, which has been input, into an ultrasonic signal and emits the ultrasonic signal to a medium, such as water or a living organism, and then converts an ultrasonic signal being input from the medium into a high frequency electric signal and outputs the high frequency electric signal.
This transducer array 1000 serves as the ultra sound transmission/reception surface of an ultrasonic probe (not shown), and is formed with a number of ultrasonic transducers 100, described above, on a substrate 1, the ultrasonic transducer 100 being connected by connections 13 by the unit of a predetermined number. The number of the ultrasonic transducers 100 is not limited to the number shown, and ultrasonic transducers 100 in an even greater number may be integrated on a larger substrate 1, depending on a semiconductor manufacturing technology. Individual ultrasonic transducers 100 or ultrasonic transducers 100 bundled by a unit of predetermined number are connected through a transmission and reception switch to a transmission beam-former and a reception beam-former (both not shown) of an ultrasonic imaging device provided with this ultrasonic probe, and acts as a phased array to be utilized for transmission and reception of ultra sounds. The shown array of the ultrasonic transducer 100 is an example, and other forms of arrays may be arranged, including a honeycomb shape and grid shape. Further, the array surface may be either a flat surface or curved surface, and the outline of the surface may be formed in a circle shape, polygonal shape, or the like. Or, the ultrasonic transducers 100 may be disposed on a line or a curve.
This ultrasonic probe is provided with a transducer array 1000 formed, for example, in an array shape having a plurality of groups of ultrasonic transducers 100 arrayed on a line, or formed in a convex type having a plurality of ultrasonic transducers 100 arrayed in a fan shape. Further, on the medium (specimen) side of the ultrasonic transducers 100 of this ultrasonic probe, there are arranged an acoustic lens for convergence of ultrasonic beams, and an acoustic matching layer for matching the acoustic impedance between the ultrasonic transducers 100 and the medium (specimen). Further, on the back side (reverse side with respect to the medium side), a packing member for absorbing propagation of ultrasonic waves is arranged.
One of the significant basic characteristics of an ultrasonic transducer 100 is gain G. Gain G means the efficiency of mutual conversion between electric energy and mechanical energy, such as mechanical energy of a sound wave. Accordingly, in view of increasing the transmission efficiency and detecting faint sound wave signals, gain G of the ultrasonic transducers 100 is desired to be high.
Further, another one of the significant characteristics of the ultrasonic transducers 100 is the fractional bandwidth fh. The greater the fractional bandwidth fh, the wider the usable frequency range, and thus a single ultrasonic transducer 100 can be used for various purposes, which is an advantage of the ultrasonic transducer 100. Further, if the fractional band width fh is greater, ultrasonic pulses with narrower pulse widths (in other words, the occupied frequency band width is wider) can be formed, which is an advantage achieving high distance resolution in ultrasonic imaging.
However, as derived from the energy conservation law, the height of sensitivity G and the width of fractional bandwidth fh contradict with each other. Therefore, in designing an ultrasonic transducer 100, it is important to be able to select a combination of a desired center frequency fc and fractional band width fh within this limitation.
Since an ultrasonic transducer 100 is a diaphragm type, the center frequency fc and the resonance frequency fb are substantially the same. The resonance frequency fb, stiffness D and mass m of a diaphragm 5 have relationship in Expression (1). Fractional band width fh has a relationship in Expression (2).
The stiffness D and mass m of a diaphragm 5 are defined by the planar shape and thickness thereof when the material is determined in advance. Accordingly, if both the planar shape and the thickness of the diaphragm 5 can be properly set, a desired frequency spectrum (combination of the center frequency fc (≅ resonance frequency fb) and the fractional band width fh) can be obtained.
The beam 7 is in a rectangular solid shape with a width of w, length of v and thickness of t when no force is applied. The stiffness D in the thickness direction (oscillation direction of the diaphragm 5: z direction) of the beam 7 has the following relation in Expression (6), wherein the mass of the beam 7 is represented by m, and the Young's Module is represented by E.
On the other hand, the mass m of the beam 7 is obtained by the following Expression (7), wherein the density is represented by ρ.
m=ρwvt (7)
The resonance frequency fb in the thickness direction t (z direction; oscillation direction of the diaphragm 5) of the beam 7 has the relationship of the following Expression (8).
f
b
2
∝D/m=Et
2/(ρv4) (8)
Therefore, the resonance frequency fb of the beam 7 is proportional to the thickness t.
Further, the fractional band width fh is proportional to the attenuation constant ζ, and the attenuation constant ζ has the relationship in the following Expression (9).
ζ∝1/√{square root over (Dm)} (9)
Herein, if Expression (8) is assigned to Expression (9), the following Equation (10) is obtained.
ζ∝1/(fbm) (10)
From this Expression (10), it is understood that the attenuation constant ζ is inversely proportional to the mass m of the beam 7 when the resonance frequency fb is constant. That is, it is understood that the fractional band width fh is inversely proportional to the thickness t when the width w and the length v are determined in advance.
In order to realize a desired resonance frequency fb of a beam 7 in a rectangular solid shape, the thickness t is uniquely determined, when the planar shape (width w and length v) is determined in advance. Further, if the material and respective dimensions of the beam 7 are determined, then the mass m is also determined, and thereby the fractional band width fh is also uniquely determined. Still further, this description on the beam 7 is also true in the case of parts which can be assumed to be a rectangular homogeneous solid shape, for example, the oscillating part 5c (the flat shaped portion excluding the beams 7) of the diaphragm 5.
As shown in
The length (dimension in y direction) of the base plate 20a and beam 7d of the oscillating body 6a and the length of the base plate 20b of the oscillating body 6b are both v. The both widths (dimension in x direction) of the base plate 20a and the base plate 20b are w1, and the width (dimension in x direction) of the beam 7d is w2. The materials of the base plate 20a, base plate 20b, and beam 7d are all the same.
Each solid graph represents the value of the resonance frequency fb of oscillating bodies 6a in accordance with the invention normalized by the resonance frequency fb of an oscillating body 6b of a comparative example. The numeral given to each solid graph indicates the value of a normalized resonance frequency fb, wherein the values of normalized resonance frequencies fb are all the same at arbitrary positions on a same solid graph.
Each dashed graph represents the fractional bandwidth fh of oscillating bodies 6a in accordance with the invention normalized by the fractional bandwidth fb of the oscillating body 6b of the comparative example. The numeral given to each dashed graph indicates the value of a normalized fractional bandwidth fh, wherein the values of normalized fractional bandwidths fh are all the same at arbitrary positions on a same dashed line.
For example, when a beam 7d is not provided on an oscillating body 6a in accordance with the invention (in other words, the thickness t2 of the beam 7d is set to zero), this oscillating body 6a is equivalent to a base plate 20b with a thickness of t0 of a comparative example. That is, the thickness ratio t1/t0 of the base plate 20a of this oscillating body 6a is set to 1.0, and the thickness ratio t2/t0 of the beam 7d is set to 0.0. Herein, in order to change the fractional bandwidth fh, having the resonance frequency fb be constant, a combination of a thickness ratio t1/t0 and a thickness ratio t2/t0 is selected such that the value of the normalized resonance frequency fb is 1.0 (moving on a solid graph given with “1.0”), and thus the thickness t1 of a base plate 20a and the thickness t2 of a beam 7d can be obtained.
Further, for example, in order to make the resonance frequency fb of an oscillating body 6a in accordance with the invention be twice as large as that of an oscillating body 6b of the comparative example and obtain a desired fractional bandwidth fh, a combination, which achieves the desired normalized value of a fractional bandwidth fh, of a thickness ratio t1/t0 and a thickness ratio t2/t0 is selected with the value of a normalized resonance frequency fb be 2.0 (moving on the solid graph given with “2.0” and finding the intersection point between this solid graph and a dashed graph given with the desired normalized value of a fractional bandwidth fh), and thus the thickness t1 of a base plate 20a and the thickness t2 of a beam 7d can be obtained.
As described above, since an oscillating body 6a has a structure provided with a beam 7d on a base plate 20a, by properly setting the respective thicknesses (dimension in z direction) of these elements (the base plate 20a and the beam 7d), a desired frequency spectrum (a combination of a resonance frequency fb and a fractional bandwidth fh) can be realized, even without changing the planar shape of these elements.
Comparison of
Specifically, when the width w2 of the beam 7d is increased having the width w1 of the base plate 20a be constant, the planar shape of the beam 7d and the planar shape of the base plate 20a become closer to each other. Accordingly, if the resonance frequency fb is maintained constant, the adjustable range of the fractional bandwidth fh achieved by selecting a combination of the thickness t1 of the base plate 20a and the thickness t2 of the beam 7d becomes narrower.
Therefore, in order to effectively change the frequency spectrum by changing the thickness t2 of the beam 7d, the width w2 of the beam 7d is made as small as possible compared with the width w1 of a base plate 20a in a range allowed by manufacturability. In the above description, the material of the base plate 20a and the material of a beam 7d are the same, however, the same effect can be achieved also using different materials.
This beam 7b is configured with a beam part 7ba with a width of w2, the beam part 7ba being a part of the beam 7b, and a beam part 7bb with a different width of w22, the beam part 7bb being another part of the beam 7b, wherein the beam parts 7ba and 7bb are joined with each other with respect to the thickness direction (z direction) with the same long axis direction. For this beam 7d, the thickness t21 of the beam part 7ba and the thickness t22 of the beam part 7bb can be selected independently. Consequently, without changing the planar shapes of the beam part 7ba and the beam part 7bb, it is possible to obtain an infinite number of combinations of the thickness t21 of the beam part 7ba and the thickness t22 of the beam part 7bb which maintain a constant ratio between the stiffness D with respect to the thickness direction and the mass m of the entire beam 7b. That is, using such a beam 7b, while having the resonance frequency fb be constant, the fractional bandwidth fh can be continuously changed by changing the combination of the thickness t21 of the beam part 7ba and the thickness t22 of the beam part 7bb.
For example, as shown in
In such a manner, the beam may have a rectangular solid shape, in other words, a shape with rectangular cross-sections in the short and long axis directions, or any other shape as long as the thickness (dimension along the oscillation direction of the diaphragm 5, namely, z direction) can be controlled during a manufacturing process. For example, the beam may have a cross-section in a polygonal shape, such as a triangular, rectangular, trapezoidal or another quadrilateral shape, or a cross-section, such as a circular, ellipsoidal shape or the like, or a cross-section which changes along a certain direction.
Next, referring to
This ultrasonic transducer 100b has the same effects as in the third embodiment, and allows the surfaces of the diaphragm 5 to be flat.
This ultrasonic transducer 100c has a structure having beams 7 implanted in the substrate of a diaphragm 5 (more specifically, an outer diaphragm layer 5b). These beams 7 are formed of a material having a higher stiffness (the Young's Module) than that of the diaphragm 5 or a material having a lower stiffness than that of the diaphragm 5. Or, the beams 7 may be formed by cavities with vacuum therein or with air or another kind of gas charged therein.
In this ultrasonic transducer 100c, the direction and the amplitude of the stiffness of the diaphragm 5 can be adjusted as desired to change the stiffness, without changing the shape or thickness of the diaphragm 5. Further, the electro-acoustic efficiency can be increased by narrowing the distance between the electrode 2 and electrode 3.
Herein, the beams 7 may be formed directly inside the inner diaphragm layer 5a or the outer diaphragm layer 5b, or may be formed by arranging recessions on the surface of the inner diaphragm layer 5a or the outer diaphragm layer 5b and joining the inner diaphragm layer 5a and the outer diaphragm layer 5b to seal these recessions.
In this ultrasonic transducer 100d, since the beam parts 7za and the electrode-layer part 7zb can be formed as a single body, the manufacturing process can be simplified and the structure can be hardened.
Further, this ultrasonic transducer 100d may have a structure which secures the most of the stiffness of the diaphragm 5 by the beam 7z serving also as an electrode and either the inner diaphragm layer 5a or the outer diaphragm layer 5b. Accordingly, either the inner diaphragm layer 5a or the outer diaphragm layer 5b is not required to take the role of securing the stiffness, and can be thinned or omitted. If the beam 7z secures most of the stiffness, the inner diaphragm 5a is unnecessary in principle. This allows narrowing the distance between the electrode 2 and the electrode 3 and improving the electro-acoustic conversion efficiency.
Or, from the point of view of protecting the beam 7z against, or insulating the beam 7z from, an external object (not shown), the outer diaphragm layer 5b may have a thickness enough for protection or insulation. By thinning the outer diaphragm layer 5b, the manufacturing process can be simplified, and the distance between the electro-acoustic conversion section, configured by the beam 7z and the electrode 2 on the substrate 1 side, and a measured medium (not shown) can be shortened, which improves the sensitivity.
Instead of the beams 7 in the third embodiment, this ultrasonic transducer 100e has a structure having a beam 7n formed of a material with a lower stiffness than that of a diaphragm 5 or formed as a cavity, adjacent to the portion where the diaphragm 5 supports itself on the electrode 2 on the substrate 1 side. In other words, this portion is a ring shaped potion inside the diaphragm 5 and is located above the marginal portion of the cavity 4, and is also a portion enclosing the oscillating part 5c of the diaphragm 5.
In this ultrasonic transducer 100e, the beam 7n lowers the stiffness of the marginal portion of the oscillating part 5c of the diaphragm 5, and thereby the stiffness of the entire oscillating part 5c improves relatively.
It is understood that this ultrasonic transducer 100e has a structure where a support 5d holds the diaphragm 5n (shown by the solid curves) on the electrode 2 on the surface of the substrate 1. For comparison, a diaphragm 5m in a case where the beam 7n is not provided is shown by the dashed curves.
In this ultrasonic transducer 100e, when the diaphragm 5 oscillates upon transmission and reception of ultra sound, the diaphragm 5 is deformed greatly in the vicinity of the beam 7n, however, the entire oscillating part 5c of the diaphragm 5 (shown as diaphragm 5n) is uniformly displaced overall while a satisfactory flatness thereof is maintained. Therefore, the average displacement amount of the diaphragm 5 can be made large even without changing the maximum displacement amount, and also, it is possible to reduce the thickness (the length in z direction) of the cavity 4 and the distance between the electrode 2 and the electrode 3. In such a manner, the electro-acoustic conversion efficiency can be improved, and a high sensitivity and high output can be realized.
In comparison of the diaphragm 5n provided with this beam 7n and the diaphragm 5m not provided with the beam 7n, it is understood that the deflection of the diaphragm 5n is small and the central portion thereof hardly contacts the electrode 2 on the substrate 1.
An ultrasonic transducer 100f (not shown) in the eighth embodiment has a structure having an outer diaphragm layer 5p instead of the above described outer diaphragm layer 5b.
This outer diaphragm layer 5p is provided with a number of beams 7p in a hole (or hollow) shape at the marginal portion of a planar shape. Similarly to the above described beam 7n, these many beams 7p lower the stiffness of the marginal portion of the outer diaphragm layer 5p and relatively improve the stiffness of the planar portion enclosed by the beams 7p.
Thus, with this ultrasonic transducer 100f in the eighth embodiment, the same effects as the ultrasonic transducer 100e in the seventh embodiment can be achieved.
This ultrasonic transducer 100g includes a circular diaphragm 5g, radial beams 7gr disposed radially on the top surface of the diaphragm 5g, and an annular beam 7gc disposed likewise. Herein, the diaphragm 5g may be in an ellipse shape.
This ultrasonic transducer 100h includes a diaphragm 5h in a hexagonal shape, radial beams 7hr disposed radially on the top surface of the diaphragm 5h, and a cell shaped beam 7hc disposed along the inner margin of the diaphragm 5h likewise. The hexagonal shape is an example, and the shape of the diaphragm 5h may be a triangle, pentagon, heptagon, or another polygon.
As examples, the above described radial beams 7gr are provided in a quantity of four (in eight directions from the center) in the ninth embodiment, and the above described radial beams 7hr are provided in a quantity of three (in six directions from the center) in the tenth embodiment. However, a suitable number of such beams may be provided, depending on the shapes of the diaphragms 5g and 5h, desired frequency spectrum and the like. Further, in the cases described in the ninth embodiment and the tenth embodiment, the annular beam 7gc in the ninth embodiment and the cell shaped beam 7hc in the tenth embodiment are provided respectively in a single quantity, as examples. However, a suitable number of such beams may be provided, concentrically for example, depending on the shapes of the diaphragms 5g and 5h, desired frequency spectrum and the like.
This ultrasonic transducer 100i has a structure having plural beams 7 which are elongated in y direction and disposed at uneven intervals.
In the ultrasonic transducer 100i in the eleventh embodiment, the distribution of stiffness of the oscillating part 5c of a diaphragm 5 can be partially adjusted and an oscillation mode can be desirably inhibited or excited, by suitably setting the pitches of disposing the plural beams 7.
This ultrasonic transducer 100j has a structure having a beam 7x which is elongated in x direction and shorter in the long axis direction thereof than the length in x direction of an oscillating part 5c of a diaphragm 5, beams 7y which are elongated in y direction and shorter in the long axis direction thereof than the length in y direction of the oscillating part 5c of the diaphragm 5, the beams 7x and 7y being arranged on an outer diaphragm layer 5b.
In such a manner, the beam 7x and 7y having different long axis directions may be disposed in mixture at different positions on the same diaphragm 5. Further, the beams 7x and 7y may have lengths shorter than the planar dimensions of the oscillating part 5c, depending on the purpose. Still further, the dimensions of the beams 7x and 7y may be different from each other.
With the ultrasonic transducer 110j in the twelfth embodiment, an oscillation mode/modes can be desirably inhibited or excited for each part of the oscillating part 5c, by suitably setting the positions, pitches, quantity of the beams 7y and 7x.
This ultrasonic transducer 100k has a structure having beams 7i, 7j and 7k which are elongated in y direction, have different cross-sections perpendicular to the long axis, and are disposed in mixture on a diaphragm 5.
In this example, on the diaphragm 5, the beams 7i having the largest cross-section are disposed adjacent to the center of the diaphragm 5, the beams 7j having a smaller cross-section than the beams 7i are disposed outside the beams 7i, and the beams 7k having a smaller cross-section than the beams 7j are disposed outside the beams 7j. Thus, the stiffness of the portion in the vicinity of the center of the diaphragm 5 is greatly reinforced while the stiffness is less reinforced toward the marginal portion of the diaphragm 5. This disposition is an example and the order of disposing the beams 7i, 7j and 7k may be changed.
With the ultrasonic transducer 100k in the thirteenth embodiment, the distribution of stiffness of the diaphragm 5 can be adjusted, and thereby, desired oscillation modes and resonance frequencies f for the respective oscillation modes can be obtained.
This ultrasonic transducer 1001 has a structure having a beam 7q elongated in x direction (horizontal direction in the figure) and beams 7r elongated in y direction (vertical direction in the figure) on the top surface of an outer diaphragm layer 5b.
In this ultrasonic transducer 1001, the stiffness of the diaphragm 5 with respect to x direction (horizontal direction in the figure) can be changed by the horizontally elongated beam 7q, and also, the stiffness of the diaphragm 5 with respect to y direction (vertical direction in the figure) can be changed by the vertically elongated beams 7r. Accordingly, even when the planar shape and dimensions of the oscillating part 5c of the diaphragm 5 are predetermined, it is possible to independently and arbitrarily set the resonance frequency fbx of an oscillation mode in x direction and the resonance frequency fby of an oscillation mode in y direction.
In this ultrasonic transducer 1001, the planar shape of the oscillating part 5c of the diaphragm 5 is substantially a square shape. However, the stiffness of this oscillating part 5c is reinforced by the single beam 7q elongated in x direction and the three beams 7r elongated in y direction. Herein, assuming that the stiffness of the beam 7q and the stiffness of each of the beams 7r are equal to each other, the oscillating part 5c of the diaphragm 5 has a small stiffness in x direction and a large stiffness in y direction despite the substantially square shape thereof.
Thus, by changing the stiffness (cross-sectional area in the short axis direction, material or the like), disposition direction, quantities and the like of beams 7q and 7r, it is possible to set desired oscillation modes and desired resonance frequencies f for the respective oscillation modes. Herein, the beam 7q and each beam 7r may be joined with each other, or may intersect with each other in stories with respect to z direction (perpendicular direction to the sheet of the figure).
By the ultrasonic transducers 100, 100b to 1001 in the respective embodiments, the following effects can be obtained, for example.
(1) Since beams (beam 7 and the like) are arranged for diaphragms (diaphragm 5 and the like), the thickness of a diaphragm (diaphragm 5 or the like) and the thickness of a beam (beam 7 or the like) can be independently changed, and the balance between the stiffness and the mass of the oscillating part 5c can be set freely, which allows control of the sensitivity G and fractional bandwidth fh, achieving a desired center frequency fc.
(2) By adjusting the thickness of a diaphragm (diaphragm 5 or the like) and the thickness of a beam (beam 7 or the like), the frequency spectrum (resonance frequency fb and fractional bandwidth fh) of the diaphragm (diaphragm 5 or the like) can be changed without changing the planar shape (longitudinal and lateral dimensions) of the diaphragm (diaphragm 5 or the like) and the beam (beam 7 or the like).
(3) Since the frequency spectrum can be changed without changing the planar shape (dimensions in x and y directions) of a diaphragm (diaphragm 5 or the like) and a beam (beam 7 or the like), flexible manufacturing can be carried out using the same manufacturing equipment and the same mask (not shown) by changing the control of a manufacturing process, allowing reduction in time and cost.
Next, a comparative example will be described, referring to
This ultrasonic transducer 100p has the same structure as the ultrasonic transducer 100 (refer to
A notch (an area where gain G rapidly drops) appears near 0.8 MHz on the graph. Accordingly, there is a problem that the value of the frequency versus gain response of the diaphragm 5 is not flat. This notch is generated by the bonding between the lateral oscillation mode and the longitudinal oscillation mode. Therefore, it is understood that one of the oscillation modes can be inhibited and thereby notch is restricted by changing the longitudinal and/or lateral stiffness.
For example, instead of setting the ratio of longitudinal length to lateral length to 1:2, by making the ratio of longitudinal length to lateral length extremely large or small (in other words, making the planar shape of the diaphragm 5 extremely elongated), it is expected that affect by either the longitudinal oscillation mode or the lateral oscillation mode is substantially eliminated, notch is restricted, and a flat frequency spectrum can be obtained over a broadband. However, a diaphragm 5 with a ratio of longitudinal length to lateral length which is extremely large or small enough to restrict notch has problems of extreme difficulty of manufacturing and impracticability.
The inventors produced design examples of the ultrasonic transducer 100 (refer to
For both the ultrasonic transducers 100 and 100p, the substrate 1 is formed of silicon, the diaphragm 5 is formed of silicon nitride, and the electrodes 2 and 3 are formed of aluminum. The vertical dimension (up-and-down direction, namely y direction, in
For the ultrasonic transducer 100 in the third embodiment, the width w of the beams 7 was set to 20 percent of the pitch between the beams 7. In order to have the resonance frequency fb of the diaphragm 5 in the third embodiment be the same as that of the diaphragm 5 in the comparative example and make the fractional bandwidth fh of the diaphragm 5 in the third embodiment is 1.5 times as wide as that in the comparative example, and based on the calculation result (refer to
For the ultrasonic transducer 100p of the comparative example, the cavity 4 above the electrode 2 on the substrate 1 side was formed 300 nm thick, and the inner diaphragm layer 5a was formed 200 nm thick. The electrode 3 on the diaphragm 5 side was formed 400 nm thick, and the outer diaphragm layer 5b was formed 2000 nm thick.
The value of frequency f is indicated in the horizontal axis direction, and the value of gain G is indicated in the vertical axis direction in a logarithmic scale. A graph 31 represents measured values with the ultrasonic transducer 100 in the third embodiment, and a curve 30 represents measured values with the ultrasonic transducer 100p of the comparative example.
For the ultrasonic transducer 100 in the third embodiment, the center frequency fc was 15.4 MHz and the fractional bandwidth fh was 157%.
For the ultrasonic transducer 100p in the comparative example, the center frequency fc was 14.8 MHz and the fractional bandwidth fh was 120%.
Accordingly, it is understood that, when compared with the ultrasonic transducer 100p of the comparative example, the ultrasonic transducer 100 in the third embodiment maintains the substantially same value of the center frequency fc, and shows a greater value of the fractional band width fh. This result agree with the tendency of the above described calculated result.
According to the calculation result (refer to
There is no practical problem with such a minor difference in most cases. However, for a more accurate calculation result, further accurate calculation may be performed, taking into account effects by other elements, such as the electrode 3, or, a prototype may be produced to adjust calculated values, based on quantitative understanding of the difference between measured values of the prototype and calculated values.
Number | Date | Country | Kind |
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2005-303701 | Oct 2005 | JP | national |
2006-056541 | Mar 2006 | JP | national |
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/JP2006/315314 | 8/2/2006 | WO | 00 | 7/31/2009 |